Burger has a broken rib while de Jongh suffered a hairline fracture to his left ankle. Experienced centre Adi Jacobs, who had been called up as a precaution, has been drafted into the tour squad as a replacement for de Jongh.
Burger is replaced by the uncapped Deon Stegmann of the Blue Bulls, while his team-mate Zane Kirchner has also been added to squad to restore the party to 30.
South Africa head coach Peter de Villiers said: "It's a blow to lose players but we've rolled with the punch and already moved on.
"We trained without them this morning and we already had contingency plans in mind which we've begun to put into operation.
"It's not an ideal situation but we've all got on with our jobs and are focused only on the players that we have in camp."
Meanwhile, former Munster centre Jean de Villiers (groin), Willem Alberts (calf) and Chiliboy Ralepelle (flu) took no part in either of the Springboks' two pitch sessions on Monday.
The South African team and replacements for the GUINNESS Series Test against Ireland will now be named on Thursday due to the injury disruptions.
"We'll give the players some more time in rehab before we confirm the team," added de Villiers, whose side lost 15-10 to Ireland at Croke Park last November.
"We have the line-up in mind but want to make sure everyone's okay before making the announcement."
The latest withdrawals take to 13 the number of players who have been forced out of the'Boks' end of year tour by injury.
The absentees are regular captain John Smit, who is recovering from a neck operation, Jaque Fourie, Wynand Olivier, Andries Bekker, Fourie du Preez, Heinrich Brüssow, JP Pietersen, Gurthrö Steenkamp, Butch James, Ulster prop BJ Botha, Ricky Januarie, Burger and de Jongh.
SOUTH AFRICA Squad - Backs (13): Gio Aplon (Western Province), Bjorn Basson (Blue Bulls), Jean de Villiers (Western Province), Francois Hougaard (Blue Bulls), Bryan Habana (Western Province), Adi Jacobs (Sharks), Elton Jantjies (Golden Lions), Zane Kirchner (Blue Bulls), Patrick Lambie (Sharks), Lwazi Mvovo (Sharks), Ruan Pienaar (Ulster), Francois Steyn (Racing Metro), Morne Steyn (Blue Bulls).
Forwards (17): Willem Alberts (Sharks), Bakkies Botha (Blue Bulls), Keegan Daniel (Sharks), Bismarck du Plessis (Sharks), Jannie du Plessis (Sharks), Alistair Hargreaves (Sharks), Ryan Kankowski (Sharks), Victor Matfield (Blue Bulls) (capt), Tendai Mtawarira (Sharks), Coenie Oosthuizen (Cheetahs), Chiliboy Ralepelle (Blue Bulls), Juan Smith (Cheetahs), Pierre Spies (Blue Bulls), Deon Stegmann (Blue Bulls), Adriaan Strauss (Cheetahs), CJ van der Linde (Cheetahs), Flip van der Merwe (Blue Bulls).